Identity and harmony

Read, Stephen

doi:10.1111/j.1467-8284.2004.00469.x

Cited by 16 publications

(26 citation statements)

References 3 publications

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“…This seems plausible on the isomorphism-invariance view, where logical truths are taken to be completely topic-neutral, whereas mathematical truths may rely on the existence of particular objects. 21 (…”

Section: The Indeterminacy Of Chmentioning

confidence: 99%

“…Our reply is twofold. First, the logical status of identity is widely accepted and largely uncontentious; several theoretical accounts of logical constanthood endorse it as logical, including not just isomorphism invariance but also inferentialist accounts such as [21] and [17]; and the arguments against identity being logical are thin on the ground and unpersuasive. Nevertheless, we recognise that in this context our first reply is dialectically controversial.…”

Section: Ch Is Logically Expressiblementioning

confidence: 99%

“… Paseau ([19], p. 46) considers this sort of argument in his response to Etchemendy 21. The proponent of isomorphism invariance should reject the converse, since it is once again logicist in flavour and so fits poorly with invariance criteria.…”

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confidence: 99%

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Isomorphism Invariance and Overgeneration

Griffiths¹,

Paseau²

2016

Bull. symb. log

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Abstract. The isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thought that logic is distinctively general or topic neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of 'logical constant' which respects the intuitively clear cases. Despite its attractions, the criterion has recently come under attack. Critics such as Feferman, MacFarlane and Bonnay argue that the criterion overgenerates by incorrectly judging mathematical notions as logical. We consider five possible precisifications of the overgeneration argument and find them all unconvincing.The standard approach to logical consequence in the modern literature is the post-Tarskian model-theoretic conception. On this conception, a sentence φ is a logical consequence of some set of sentences Γ just if every model of Γ is a model of φ. A model consists of a nonempty domain of objects and a valuation function that assigns semantic values to the nonlogical expressions of the language. As such, the standard approach relies on a distinction between logical and nonlogical expressions. It is striking, then, that there is little agreement over how this crucial distinction should be drawn. We defend the most natural supplement to the model-theoretic definition: isomorphism invariance.The isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thoughts that logic is distinctively general or topic-neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of 'logical constant' which respects the intuitively clear cases, namely identity, the Boolean connectives and the universal and existential quantifiers-the logical constants of first-order logic with identity.Despite its attractions, isomorphism invariance faces a major recurring objection in the literature.

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Section: The Indeterminacy Of Chmentioning

confidence: 99%

Section: Ch Is Logically Expressiblementioning

confidence: 99%

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Isomorphism Invariance and Overgeneration

Griffiths¹,

Paseau²

2016

Bull. symb. log

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“…This is a bold claim, and one that needs to be examined with care. Much was wrong, indeed, with the treatment of identity in Read (2004), 17 or rather with its articulation, for, as I will argue, the basic idea was correct. There are also major problems with Griffiths' arguments.…”

mentioning

confidence: 98%

“…Identity. In a recent article, Griffiths (2014) challenges this proposal, with specific reference to rules proposed in Read (2004) for identity. Griffiths (2014, §7) claims that if a connective is defined by inharmonious rules, then harmonious rules cannot be given for it.…”

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confidence: 99%

Harmonic Inferentialism and the Logic of Identity

Read

2016

The Review of Symbolic Logic

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Abstract. Inferentialism claims that the rules for the use of an expression express its meaning without any need to invoke meanings or denotations for them. Logical inferentialism endorses inferentialism specifically for the logical constants. Harmonic inferentialism, as the term is introduced here, usually but not necessarily a subbranch of logical inferentialism, follows Gentzen in proposing that it is the introduction-rules whch give expressions their meaning and the elimination-rules should accord harmoniously with the meaning so given. It is proposed here that the logical expressions are those which can be given schematic rules that lie in a specific sort of harmony, general-elimination (ge) harmony, resulting from applying a certain operation, the ge-procedure, to produce ge-rules in accord with the meaning defined by the I-rules. Griffiths (2014) claims that identity cannot be given such rules, concluding that logical inferentialists are committed to ruling identity a non-logical expression. It is shown that the schematic rules for identity given in Read (2004), slightly amended, are indeed ge-harmonious, so confirming that identity is a logical notion.

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Meaning, Use, Verification

Skorupski¹

2017

A Companion to the Philosophy of Language

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Identity and harmony

Cited by 16 publications

References 3 publications

Isomorphism Invariance and Overgeneration

Isomorphism Invariance and Overgeneration

Harmonic Inferentialism and the Logic of Identity

Meaning, Use, Verification

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